Question
A plane meets the co-ordinate axes at A, B, C such that the centroid of triangle ABC is the point (a, b, c). Show that the equation of the plane is 
Solution
Let the equation of plane be 
....(1)
It meets x-axis in A where y = 0, z = 0
Putting y = 0, z = 0 in (1), we get x / α = 1, ∴ x = α
∴ A is (α, 0, 0)
Similarly B, C are (0,β, 0), (0, 0, γ) respectively
∴ (a, b, c) is centroid of triangle ABC
Putting values of α, β, γ in (1), we get,
or
which is required equation of plane
....(1)It meets x-axis in A where y = 0, z = 0
Putting y = 0, z = 0 in (1), we get x / α = 1, ∴ x = α
∴ A is (α, 0, 0)
Similarly B, C are (0,β, 0), (0, 0, γ) respectively
∴ (a, b, c) is centroid of triangle ABC
Putting values of α, β, γ in (1), we get,
or
which is required equation of plane
